Uncertainties in Climatological Seawater Density Calculations

Abstract

In most applications, with seawater conductivity, temperature, and pressure data measured in situ by various observation instruments e.g., Conductivity‐Temperature‐Depth instruments (CTD), the density which has strong ties to ocean dynamics and so on is computed according to equations of state for seawater. This paper, based on density computational formulae in the Thermodynamic Equation of Seawater 2010 (TEOS‐10), follows the Guide of the expression of Uncertainty in Measurement (GUM) and assesses the main sources of uncertainties. By virtue of climatological decades‐average temperature/Practical Salinity/pressure data sets in the global ocean provided by the National Oceanic and Atmospheric Administration (NOAA), correlation coefficients between uncertainty sources are determined and the combined standard uncertainties uctrue(ρtrue) in seawater density calculations are evaluated. For grid points in the world ocean with 0.25° resolution, the standard deviations of uctrue(ρtrue) in vertical profiles cover the magnitude order of 10−4 kg m−3. The uctrue(ρtrue) means in vertical profiles of the Baltic Sea are about 0.028kg m−3 due to the larger scatter of Absolute Salinity anomaly. The distribution of the uctrue(ρtrue) means in vertical profiles of the world ocean except for the Baltic Sea, which covers the range of true(0.004,0.01true) kg m−3, is related to the correlation coefficient rtrue(SA,ptrue) between Absolute Salinity SA and pressure p. The results in the paper are based on sensors' measuring uncertainties of high accuracy CTD. Larger uncertainties in density calculations may arise if connected with lower sensors' specifications. This work may provide valuable uncertainty information required for reliability considerations of ocean circulation and global climate models.

Agulhas Ring Heat Content and Transport in the South Atlantic Estimated by Combining Satellite Altimetry and Argo Profiling Floats Data

“…For density, an estimation can be obtained using the law of propagation of uncertainty (BIPM, 2008) in the linear equation of state for sea water. For example, the uncertainty of 0.005 kg m −3 for ρ obtained by Dai and Zhang (2018) is very close to the one of 0.004 kg m −3 obtained applying this method to their uncertainties for Θ and S A . Thus, our estimation of the accuracy computed in the Argo profiles result into uncertainties of about 0.07 g kg −1 for S A , 0.02°C for Θ, and about 0.05 kg m −3 for σ 0 that we assume to be similar for ρ.…”

“…By following the Guide to the expression of uncertainty in measurement (GUM) (BIPM, 2008), Dai and Zhang (2018) assessed the main sources of uncertainties converting in situ measurements of the former version of the 0.25°× 0.25°decades-average WOA (1955-2012) using the GSW Oceanographic Toolbox. By detailing the different uncertainty components, they obtained a vertically averaged mean uncertainty in the off-shore part of the Southern Atlantic of about 1.4 db for pressure, about 0.005 g kg −1 for S A (using 0.0017 psu for S P ), about 0.002°C for Θ (using 0.002°C for T) and about 0.005 kg m −3 for density (ρ).…”

“…As the complete computation of uncertainties is out of the scope of this study, we give an estimate of the resulting uncertainty. For Θ, the uncertainties obtained by Dai and Zhang (2018) are equal to the one for T. However, due to the dependence on S A that have uncertainties of 1 order of magnitude larger in Delayed Mode Argo, we would like to be conservative by defining a large uncertainty of 0.02°C for Θ (i.e., 10 times the one for T). For density, an estimation can be obtained using the law of propagation of uncertainty (BIPM, 2008) in the linear equation of state for sea water.…”

Observations of Tidal Modulation on Diurnal Vertical Displacements of the Oceanic Transition Layer

“…As detailed in the SBE 911plus CTD manual (https://www. seabird.com/sbe-911plus-ctd/product-downloads?id=60761421595), the measurement uncertainties in temperature and conductivity stand at 0.001°C and 0.3 mS/m, resulting in an uncertainty of ∼0.001 kg/m 3 for density (Dai & Zhang, 2018). In light of the observed error velocity and RDI 300k ADCP manual (https://www.comm-tec.com/Docs/Manuali/RDI/BBPRIME.…”

“…The potential density was calculated using potential temperature and salinity (GSW oceanographic toolbox, McDougall and Barker (2011)). As detailed in the SBE 911plus CTD manual (https://www.seabird.com/sbe-911plus-ctd/product-downloads?id=60761421595), the measurement uncertainties in temperature and conductivity stand at 0.001°C and 0.3 mS/m, resulting in an uncertainty of ∼0.001 kg/m 3 for density (Dai & Zhang, 2018). In light of the observed error velocity and RDI 300k ADCP manual (https://www.comm-tec.com/Docs/Manuali/RDI/BBPRIME.pdf), the random error of measured velocity was estimated to be 0.02 m/s.…”